Quantifier Elimination for the Relative Frobenius
by
Thomas Scanlon
Berkeley

Let (K, v) be a complete discretely valued field of mixed characteristic with an algebraically closed residue field. Equip K with a continuous automorphism \sigma: K --> K lifting the Frobenius in the sense that \sigma(x) \equiv x^p (mod m_K) for x in O_K. The structure (K, v, \sigma) does not admit elimination of quantifiers in the language of valued difference fields, but it does in natural expansions involving additive-multiplicative-congruences or angular component functions.

I plan to explain the meaning of this theorem in detail and sketch a proof based on a reduction to a quantifier elimination theorem for general valued difference and differential field of equicharacteristic zero.

Date received: July 12, 1999